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If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?
- a)x is divisible by 3.
- b)3x is divisible by 10.
- c)x − 1 is divisible by 5.
- d)x is odd.
- e)3x is even.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If x is a positive integer and 3x + 2 is divisible by 5, then which of...
To determine which statement must be true, let's analyze the given information and the answer choices.
We are given that 3x + 2 is divisible by 5. In other words, there exists an integer k such that 3x + 2 = 5k.
Let's examine each answer choice:
(A) x is divisible by 3.
If x is divisible by 3, then we can write x as 3m for some integer m. Substituting this into our equation, we get 3(3m) + 2 = 5k, which simplifies to 9m + 2 = 5k. This equation does not provide any information about the divisibility of k by 5, so we cannot conclude that x is divisible by 3 based on the given information.
If x is divisible by 3, then we can write x as 3m for some integer m. Substituting this into our equation, we get 3(3m) + 2 = 5k, which simplifies to 9m + 2 = 5k. This equation does not provide any information about the divisibility of k by 5, so we cannot conclude that x is divisible by 3 based on the given information.
(B) 3x is divisible by 10.
If 3x is divisible by 10, then we can write 3x as 10n for some integer n. Substituting this into our equation, we get 10n + 2 = 5k, which simplifies to 2n + 2 = 5k. This equation does not provide any information about the divisibility of k by 5, so we cannot conclude that 3x is divisible by 10 based on the given information.
If 3x is divisible by 10, then we can write 3x as 10n for some integer n. Substituting this into our equation, we get 10n + 2 = 5k, which simplifies to 2n + 2 = 5k. This equation does not provide any information about the divisibility of k by 5, so we cannot conclude that 3x is divisible by 10 based on the given information.
(C) x - 1 is divisible by 5.
Let's analyze this statement. If x - 1 is divisible by 5, then we can write x - 1 as 5p for some integer p. Adding 1 to both sides of the equation, we get x = 5p + 1. Substituting this into our original equation, we have 3(5p + 1) + 2 = 5k, which simplifies to 15p + 5 + 2 = 5k and further simplifies to 15p + 7 = 5k. Rearranging this equation, we have 5(3p + 1) + 2 = 5k. Since the left-hand side is divisible by 5, it follows that the right-hand side (5k) must also be divisible by 5. Therefore, x - 1 being divisible by 5 is a valid conclusion based on the given information.
Let's analyze this statement. If x - 1 is divisible by 5, then we can write x - 1 as 5p for some integer p. Adding 1 to both sides of the equation, we get x = 5p + 1. Substituting this into our original equation, we have 3(5p + 1) + 2 = 5k, which simplifies to 15p + 5 + 2 = 5k and further simplifies to 15p + 7 = 5k. Rearranging this equation, we have 5(3p + 1) + 2 = 5k. Since the left-hand side is divisible by 5, it follows that the right-hand side (5k) must also be divisible by 5. Therefore, x - 1 being divisible by 5 is a valid conclusion based on the given information.
(D) x is odd.
We cannot conclude that x is odd based on the given information. For example, if x = 2, then 3x + 2 = 3(2) + 2 = 8, which is divisible by 5, but x is not odd.
We cannot conclude that x is odd based on the given information. For example, if x = 2, then 3x + 2 = 3(2) + 2 = 8, which is divisible by 5, but x is not odd.
(E) 3x is even.
We cannot conclude that 3x is even based on the given information. For example, if x = 1, then 3x + 2 = 3(1) + 2 = 5, which is divisible by 5, but 3x is not even.
We cannot conclude that 3x is even based on the given information. For example, if x = 1, then 3x + 2 = 3(1) + 2 = 5, which is divisible by 5, but 3x is not even.
Based on the analysis above, the only statement that must be true is (C) x - 1 is divisible by 5.
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Community Answer
If x is a positive integer and 3x + 2 is divisible by 5, then which of...
To determine which of the given options must be true, we can simplify the given expression and analyze its divisibility.
The expression 3x + 2 is divisible by 5 if and only if 3x is divisible by 5. So, we need to determine if x is divisible by 3.
If x is divisible by 3, then 3x will also be divisible by 3. However, if x is not divisible by 3, then 3x will also not be divisible by 3.
Therefore, we can conclude that option a) x is divisible by 3 must be true.
So, the correct answer is (a) x is divisible by 3.
The expression 3x + 2 is divisible by 5 if and only if 3x is divisible by 5. So, we need to determine if x is divisible by 3.
If x is divisible by 3, then 3x will also be divisible by 3. However, if x is not divisible by 3, then 3x will also not be divisible by 3.
Therefore, we can conclude that option a) x is divisible by 3 must be true.
So, the correct answer is (a) x is divisible by 3.
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If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?a)x is divisible by 3.b)3x is divisible by 10.c)x − 1 is divisible by 5.d)x is odd.e)3x is even.Correct answer is option 'C'. Can you explain this answer?
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